I'll try to do it... However, you will have to check by yourself if it seems correct, because I still haven't found any way to check this kind of exercises
Let A be the set of "plates containing letter J on it".
Since there is equiprobability to find a plate comparing to another :
For 1 letter, there are 26 possibilities.
For 1 integer, there are 10 possibilities (0 to 9).
Since repeats are allowed, there are possible plates. This is
Now, 1 letter is fixed to J.
So we will have to choose for 2 letters and 3 integers. Once again, repeats are allowed. Therefore, there are possible plates. This is
I know there is a shorter way, but I've been taught that we can avoid more easily mistakes by doing this way...